Besides the gold-standard of JSTOR, secondary material specifically related to the Middle East can be found on these online resources.
Arabic
Open Access Publications from the Oriental Institute (The University of Chicago)
Though dominated by titles focusing on the ancient "Orient," the list includes many publications about the medieval and modern Middle East.
A wide variety of online Arabic works on Shiism.
Turkish
İLÂHİYAT MAKALELER VERİ TABANI = ARTICLE DATABASE of ILAHIYAT / ISLAMIC STUDIES
Database of articles on Islamic Studies published by Theology Faculties in Turkey and managed by İSAM - İslam Araştırmaları Merkezi.
CEEOL - Central and Eastern European Online Library
Hosts e-books and journals in the fields of Humanities and Social Science publications from and about Central, Eastern and Southeastern Europe, including publications from Turkey.
ISAM (Turkiye Diyanet Vakfi)
ISAM Library with articles and theses databases.
Türkiye Makaleler Bibliyografyası
A searchable index to periodical articles in Turkish periodicals, from 1995 to the present.
And, of course...
JSTOR offers the back issues of journals from a range of humanities and social science disciplines, which you can search by individual title or across the entire database. You can access articles as both as images and as text. Access to journals from JSTOR is restricted to current Penn faculty, staff and students.
International periodicals in the humanities and social sciences, which include journals in English, French, German, Italian, Spanish and many other Western languages.
A multidisciplinary database of academic journals, popular magazines, and newspapers, often with full-text. You can limit your search to "area studies" to narrow to journals and other publications that are more likely to be related to Japan and Asian studies. In addition, searches can be limited by type of publication, to scholarly, peer-reviewed journals only, or to only articles with linked full text. This database offers abstracts to more than 16,000 periodicals bibliographic citations with indexing.
A database of over 2,000 journals published throughout the world including major historical journals from many countries, in addition to hundreds of journals in the social sciences and humanities. All publications featured date from 1974- present. Updated three times a year. It offers historical coverage of the world from 1450 to the present (not including the U.S. and Canada).
Digital Islam: Theses on Ethos
This searchable database contains 971 PhD theses from British institutions on Islam.
ProQuest Dissertations and Theses: UK & Ireland
Databases through which you can search for dissertations and theses. In many cases, you can download a PDF of the dissertation. These resources also include citations and some full-text research papers.